An adaptive markov chain monte carlo method for bayesian finite element model updating

Abstract: In this paper, an adaptive Markov Chain Monte Carlo (MCMC) approach for Bayesian finite element model updating is presented. This approach is known as the Adaptive Hamiltonian Monte Carlo (AHMC) approach. The convergence rate of the Hamiltonian/Hybrid Monte Carlo (HMC) algorithm is high due to its trajectory which is guided by the derivative of the posterior probability distribution function. This can lead towards high probability areas in a reasonable period of time. However, the HMC performance decreases when sampling from posterior functions of high dimension and when there are strong correlations between the uncertain parameters. The AHMC approach, a locally adaptive version of the HMC approach, allows efficient sampling from complex posterior distribution functions and in high dimensions. The efficiency and accuracy of the AHMC method are investigated by updating a real structure

Finite Element Model updating using Hamiltonian Monte Carlo techniques

Abstract: Bayesian techniques have been widely used in finite element model (FEM) updating. The attraction of these techniques is their ability to quantify and characterise the uncertainties associated with dynamic systems. In order to update an FEM, the Bayesian formulation requires the evaluation of the posterior distribution function. For large systems this function is difficult to solve analytically. In such cases the use of sampling techniques often provides a good approximation of this posterior distribution function. The hybrid Monte Carlo (HMC) method is a classic sampling method used to approximate high-dimensional complex problems. However, the acceptance rate (AR) of HMC is sensitive to the system size, as well as to the time step used to evaluate the molecular dynamics (MD) trajectory. The shadow HMC technique (SHMC), which is a modified version of the HMC method, was developed to improve sampling for large-system sizes by drawing from a modified shadow Hamiltonian function. However, the SHMC algorithm performance is limited by the use of a non-separable modified Hamiltonian function. Moreover, two additional parameters are required for the sampling procedure, which could be computationally expensive. To overcome these weaknesses the separable shadow HMC (S2HMC) method has been introduced. This method uses a transformation to a different parameter space to generate samples. In this paper we analyse the application and performance of these algorithms, including the parameters used in each algorithm, their limitations and the effects on model updating. The accuracy and the efficiency of the algorithms are demonstrated by updating the finite element models of two real mechanical structures. It is observed that the S2HMC algorithm has a number of advantages over the other algorithms; for example, the S2HMC algorithm is able to efficiently sample at larger time steps while using fewer parameters than the other algorithms

A new T-S fuzzy model predictive control for nonlinear processes

Abstract: In this paper, a novel fuzzy Generalized Predictive Control (GPC) is proposed for discrete-time nonlinear systems via Takagi-Sugeno system based Kernel Ridge Regression (TS-KRR). The TS-KRR strategy approximates the unknown nonlinear systems by learning the Takagi-Sugeno (TS) fuzzy parameters from the input-output data. Two main steps are required to construct the TS-KRR: the first step is to use a clustering algorithm such as the clustering based Particle Swarm Optimization (PSO) algorithm that separates the input data into clusters and obtains the antecedent TS fuzzy model parameters. In the second step, the consequent TS fuzzy parameters are obtained using a Kernel ridge regression algorithm. Furthermore, the TS based predictive control is created by integrating the TS-KRR into the Generalized Predictive Controller. Next, an adaptive, online, version of TS-KRR is proposed and integrated with the GPC controller resulting an efficient adaptive fuzzy generalized predictive control methodology that can deal with most of the industrial plants and has the ability to deal with disturbances and variations of the model parameters. In the adaptive TS-KRR algorithm, the antecedent parameters are initialized with a simple K-means algorithm and updated using a simple gradient algorithm. Then, the consequent parameters are obtained using the sliding-window Kernel Recursive Least squares (KRLS) algorithm. Finally, two nonlinear systems: A surge tank and Continuous Stirred Tank Reactor (CSTR) systems were used to investigate the performance of the new adaptive TS-KRR GPC controller. Furthermore, the results obtained by the adaptive TS-KRR GPC controller were compared with two other controllers. The numerical results demonstrate the reliability of the proposed adaptive TS-KRR GPC method for discrete-time nonlinear systems

Modelling Collaborative Motion in Mobile Ad Hoc Networks.

Please help us populate SUNScholar with the post print version of this article. It can be e-mailed to: [email protected]

Modelling Collaborative Motion in Mobile Ad Hoc Networks.

Please help us populate SUNScholar with the post print version of this article. It can be e-mailed to: [email protected]

Finite Element Model Updating Using the Separable Shadow Hybrid Monte Carlo Technique

ABSTRACT The use of Bayesian techniques in Finite Element Model (FEM) updating has recently increased. These techniques have the ability to quantify and characterize the uncertainties of dynamic structures. In order to update a FEM, the Bayesian formulation requires the evaluation of the posterior distribution function. For large systems, this functions is either difficult (or not available) to solve in an analytical way. In such cases using sampling techniques can provide good approximations of the Bayesian posterior distribution function. The Hybrid Monte Carlo (HMC) method is a powerful sampling method for solving higher-dimensional complex problems. The HMC uses the molecular dynamics (MD) as a global Monte Carlo (MC) move to reach areas of high probability. However, the acceptance rate of HMC is sensitive to the system size as well as the time step used to evaluate MD trajectory. To overcome this, we propose the use of the Separable Shadow hybrid Monte Carlo (S2HMC) method. This method generates samples from a separable shadow Hamiltonian. The accuracy and the efficiency of this sampling method is tested on the updating of a GARTEUR SM-AG19 structure

Finite element model updating using Hamiltonian Monte Carlo techniques

Abstract: Bayesian techniques have been widely used in finite element model (FEM) updating. The attraction of these techniques is their ability to quantify and characterise the uncertainties associated with dynamic systems. In order to update an FEM, the Bayesian formulation requires the evaluation of the posterior distribution function. For large systems this function is difficult to solve analytically. In such cases the use of sampling techniques often provides a good approximation of this posterior distribution function. The hybrid Monte Carlo (HMC) method is a classic sampling method used to approximate high-dimensional complex problems. However, the acceptance rate (AR) of HMC is sensitive to the system size, as well as to the time step used to evaluate the molecular dynamics (MD) trajectory. The shadow HMC technique (SHMC), which is a modified version of the HMC method, was developed to improve sampling for large-system sizes by drawing from a modified shadow Hamiltonian function. However, the SHMC algorithm performance is limited by the use of a non-separable modified Hamiltonian function. Moreover, two additional parameters are required for the sampling procedure, which could be computationally expensive. To overcome these weaknesses the separable shadow HMC (S2HMC) method has been introduced. This method uses a transformation to a different parameter space to generate samples. In this paper we analyse the application and performance of these algorithms, including the parameters used in each algorithm, their limitations and the effects on model updating. The accuracy and the efficiency of the algorithms are demonstrated by updating the finite element models of two real mechanical structures. It is observed that the S2HMC algorithm has a number of advantages over the other algorithms; for example, the S2HMC algorithm is able to efficiently sample at larger time steps while using fewer parameters than the other algorithms

Finite element model updating using the shadow hybrid Monte Carlo technique

Recent research in the field of finite element model updating (FEM) advocates the adoption of Bayesian analysis techniques to dealing with the uncertainties associated with these models. However, Bayesian formulations require the evaluation of the Posterior Distribution Function which may not be available in analytical form. This is the case in FEM updating. In such cases sampling methods can provide good approximations of the Posterior distribution when implemented in the Bayesian context. Markov Chain Monte Carlo (MCMC) algorithms are the most popular sampling tools used to sample probability distributions. However, the efficiency of these algorithms is affected by the complexity of the systems (the size of the parameter space). The Hybrid Monte Carlo (HMC) offers a very important MCMC approach to dealing with higher-dimensional complex problems. The HMC uses the molecular dynamics (MD) steps as the global Monte Carlo (MC) moves to reach areas of high probability where the gradient of the log-density of the Posterior acts as a guide during the search process. However, the acceptance rate of HMC is sensitive to the system size as well as the time step used to evaluate the MD trajectory. To overcome this limitation we propose the use of the Shadow Hybrid Monte Carlo (SHMC) algorithm. The SHMC algorithm is a modified version of the Hybrid Monte Carlo (HMC) and designed to improve sampling for large-system sizes and time steps. This is done by sampling from a modified Hamiltonian function instead of the normal Hamiltonian function. In this paper, the efficiency and accuracy of the SHMC method is tested on the updating of two real structures; an unsymmetrical H-shaped beam structure and a GARTEUR SM-AG19 structure and is compared to the application of the HMC algorithm on the same structures

Finite element model updating using an evolutionary Markov chain Monte Carlo algorithm

One challenge in the finite element model (FEM) updating of a physical system is to estimate the values of the uncertain model variables. For large systems with multiple parameters this requires simultaneous and efficient sampling from multiple a prior unknown distributions. A further complication is that the sampling method is constrained to search within physically realistic parameter bounds. To this end, Markov Chain Monte Carlo (MCMC) techniques are popular methods for sampling from such complex distributions. MCMC family algorithms have previously been proposed for FEM updating. Another approach to FEM updating is to generate multiple random models of a system and let these models evolve over time. Using concepts from evolution theory this evolution process can be designed to converge to a globally optimal model for the system at hand. A number of evolution-based methods for FEM updating have previously been proposed. In this paper, an Evolutionary based Markov chain Monte Carlo (EMCMC) algorithm is proposed to update finite element models. This algorithm combines the ideas of Genetic Algorithms, Simulated Annealing, and Markov Chain Monte Carlo techniques. The EMCMC is global optimisation algorithm where genetic operators such as mutation and crossover are used to design the Markov chain to obtain samples. In this paper, the feasibility, efficiency and accuracy of the EMCMC method is tested on the updating of a real structure